The game is short enough that the level design didn't bother me that much- I've beaten it with 100% map completion in under three hours; that required some clever use of tickets, btw.
LoI had more platforming than CoD, but that isn't saying much. It's almost like the designers weren't sure how to put platforming into a 3d setting or something, so they didn't really try.
And the whip-jumping was a bit silly, but can't at least one of the 2d Belmonts do something similar? Julius in HoD? So yeah. A better solution would have been to have him swing like in SCIV, but... just saying...
You get a silly picture montage of Pumpkin with the other characters while Admiration Of Clan plays in the background 
Joachim's ending was better, though Pumpkin's ending is cute.
About the story... well, Castlevania is not known for it's fantastic stories, but I think that LoI's story gets a lot of unfair hate.
As far as presentation of the story goes, the script and hammy voice acting (though they got good voice actors) did not help AT ALL. In SotN it was cheesy-charming but in LoI it was cringe-worthy. That said, I'd hope most people were able to look past that. XD
As far as plot itself goes, let's face it; we'd have been surprised if the game DIDN'T involve rescuing a DiD or brainwashing or betrayal.
Ignoring the historical inaccuracies as far as dates and the designs and names (even alchemy itself) in the game (because Castlevania is hardly historically accurate in that respect beyond making references to the real Vlad's death and such) I liked the background story given.
There should have been more information available about who Joachim was; I kind of resent the Japanese only phone manga for that. >_> It also would have been nice to know a little more about Walter and perhaps how exactly it was that Rinaldo knew Mathias' family. But that's not a big issue.
I liked how the whip was created; it gave the weapon a new, almost menacing side. The poltergeist king was only in the English version of CV3, right? Am I the only one who thinks it is kind of weird that a poltergeist king would give a family a weapon to destroy vampires with apparently no strings attached?
Now as to the controversy involving Mathias being Dracula and how he became Dracula, I thought it fit well with the 'character' of Dracula that was already established in the series. Mathias' intelligent but rash and spiteful nature was perfectly in line with everything else we'd seen in Dracula. I also don't see how it is a problem that the Dracula in Castlevania is presumably Vlad III; all it means is that at some point the guy assumed that identity.
I find this idea of Mathias using the Crimson Stone and Walter's soul to become a super-nasty vampire who then wanders off and becomes even more powerful as time goes by to be preferable to him being bitten. That just... it's just not as cool, you know? Another issue is that if vampires gain strength over time, then Dracula should not have been as powerful as he was if he was only Vlad III. LoI's explanation is logical; Vlad III/Dracula was already very old and was from the start superior in nature to the average vampire by the time Trevor and Co. faced him.
I was glad that they actually made his motivations better than just "I'm a vampire just because" and "I'm killing humans because I'm evil." It is instead "I'm a vampire opposing God because he's a douchebag" and "I'm killing humans because they are douchebags."
And finally... I am sick to death of people complaining about Legends being stripped from the canon story. The only thing Legends actually 'explained' was where Trevor Belmont came from, and that was like something out of a bad fan fiction.
I don't hear anybody whining about Circle of the Moon being stripped from the canon. You're all just haters. XD